In Algorithm 1, the perturbation mechanism regarding the model estimation (REF ) is directly come from Protocol 1. The dual update rule (REF ) draws inspiration from the local control laws [1]}, while the dual process (REF ) is essentially a Nesterov's scheme [2]}. Recalling the challenge of algorithm design, i.e., determining the local update \(u_i\left( t \right)\)  and the mappings \(\mathcal {A}_{i,t}^{k}\left( \cdot \right)\)  and \(\mathcal {C}_{i,t}\left( \cdot \right)\) , Algorithm 1 has given the specific form of \(\mathcal {A}_{i,t}^{k}\left( \cdot \right)\)  and \(\mathcal {C}_{i,t}\left( \cdot \right)\) , so next we make \(u_i\left( t \right)\)  in (REF ) explicit.
